Certificate for #15488 ⟨a, b | aaa=ab, babbb=b⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Axiom: aaa=ab.

Defines rule #4.

Referenced by [3], [5], [6].

Axiom: babbb=b.

Referenced by [4], [7], [8], [9].

Overlap of [1] aaa=ab with [1] aaa=ab:

Critical pair: aab=aba.

Flip LHS and RHS.

Referenced by [4], [6], [8].

Overlap of [3] aba=aab with [2] babbb=b:

Critical pair: ab=aabbbb.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aaa=ab with [4] aabbbb=ab:

Critical pair: aab=abbbbb.

Defines rule #3.

Referenced by [6], [8].

Overlap of [5] aab=abbbbb with [3] aba=aab:

Critical pair: aaab=abbbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] babbb=b with [6] abbbbba=abb:

Critical pair: babb=bbba.

Flip LHS and RHS.

Referenced by [8].

Overlap of [2] babbb=b with [7] bbba=babb:

Critical pair: bababb=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [2] babbb=b with [8] ba=bbbbb:

Critical pair: bbbbbbbb=b.

Defines rule #1.